Talk by Aurel Lazar, Department of Electrical Engineering, Columbia University. Given to the Redwood Center for Theoretical Neuroscience at UC Berkeley.

Abstract.

We first present a general framework for the reconstruction of natural video scenes encoded with a population of spiking neural circuits with random thresholds. The visual encoding system consists of a bank of filters, modeling the visual receptive fields, in cascade with a population of neural circuits, modeling encoding with spikes in the early visual system. The neuron models considered include integrate-and-fire neurons and ON-OFF neuron pairs with threshold-and-fire spiking mechanisms. All thresholds are assumed to be random. We show that for both time-varying and space-time-varying stimuli neural spike encoding is akin to taking noisy measurements on the stimulus. Second, we formulate the reconstruction problem as the minimization of a suitable cost functional in a finite-dimensional vector space and provide an explicit algorithm for stimulus recovery. We also present a general solution using the theory of smoothing splines in Reproducing Kernel Hilbert Spaces. We provide examples of both synthetic video as well as for natural scenes and show that the quality of the reconstruction degrades gracefully as the threshold variability of the neurons increases. Third, we demonstrate a number of simple operations on the original visual stimulus including translations, rotations and zooming. All these operations are natively executed in the spike domain. The processed spike trains are decoded for the faithful recovery of the stimulus and its transformations. Finally, we extend the above results to neural encoding circuits built with Hodgkin-Huxley neurons. References: Aurel A. Lazar, Eftychios A. Pnevmatikakis and Yiyin Zhou, Encoding Natural Scenes with Neural Circuits with Random Thresholds, Vision Research, 2010, Special Issue on Mathematical Models of Visual Coding, http://dx.doi.org/10.1016/j.visres.2010.03.015 Aurel A. Lazar, Population Encoding with Hodgkin-Huxley Neurons, IEEE Transactions on Information Theory, Volume 56, Number 2, pp. 821-837, February, 2010, Special Issue on Molecular Biology and Neuroscience, http://dx.doi.org/10.1109/TIT.2009.2037040

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